New York Laws
Title 7 - Discharge of Surety
15-701 - Surety Not Discharged by Failure or Refusal by Creditor to Sue Principal Debtor.

ยง 15-701. Surety not discharged by failure or refusal by creditor to
sue principal debtor. Unless otherwise agreed between the parties in
writing, the failure or refusal by a creditor, after a demand by a
person bound as surety, to bring an action against a principal debtor
upon a contract hereafter made or an obligation hereafter created for
the payment of money or the performance of any act shall not discharge
such surety.